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                <h1 class="title-article">Pty的字符串(string)</h1>
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<h4 class="ui top attached block header">题目描述</h4>
<div class="ui bottom attached segment font-content">
<div>
<p>在神秘的东方有一棵奇葩的树，它有一个固定的根节点（编号为1）。树的每条边上都是一个字符，字符为a,b,c中的一个，你可以从树上的任意一个点出发，然后沿着远离根的边往下行走，在任意一个节点停止，将你经过的边的字符依次写下来，就能得到一个字符串，例如：</p>
<p> </p>
<p> </p>
<p> </p>
<p>在这棵树中我们能够得到的字符串是：</p>
<p>c, cb, ca, a, b, a</p>
<p>现在pty得到了一棵树和一个字符串S。如果S的一个子串[l,r]和树上某条路径所得到的字符串完全相同，则我们称这个子串和该路径匹配。现在pty想知道，S的所有子串和树上的所有路径的匹配总数是多少？</p>
<p> </p>
<p> </p>
<p> </p>
</div>
</div>
</div>
</div>
<div class="row">
<div class="column">
<h4 class="ui top attached block header">输入格式</h4>
<div class="ui bottom attached segment font-content">
<div>
<p> </p>
<p> </p>
<p>第一行：n</p>
<p> </p>
<p> </p>
<p> </p>
<p>接下来n-1行，每行一个整数fa, 一个字符c，字符和整数之间用一个空格隔开</p>
<p> </p>
<p> </p>
<p> </p>
<p>第i行fa代表第i号节点的父亲，c表示第i号节点和fa的连边的字符</p>
<p>最后一行为字符串S</p>
<p> </p>
<p> </p>
</div>
</div>
</div>
</div>
<div class="row">
<div class="column">
<h4 class="ui top attached block header">输出格式</h4>
<div class="ui bottom attached segment font-content">
<div>
<p>输出共一行，表示匹配总数，因为评测系统暂未确定，所以C/C++选手请使用cout输出。</p>
<p> </p>
</div>
</div>
</div>
</div>
<div class="row">
<div class="column">
<h4 class="ui top attached block header">样例</h4>
<div class="ui bottom attached segment font-content">
<div>
<h4>样例输入</h4>
<div class="ui existing segment">
<pre><code class="lang-plain">5
1 c
2 b
1 a
2 a
cba</code></pre>
</div>
<h4>样例输出</h4>
<div class="ui existing segment">
<pre><code class="lang-plain">5</code></pre>
</div>
</div>
</div>
</div>
</div>
<div class="row">
<div class="column">
<h4 class="ui top attached block header">数据范围与提示</h4>
<div class="ui bottom attached segment font-content">
<div>
<p>【样例说明】</p>
<p>单个字符匹配的对数为4对，两个字符匹配的对数为1对：cb</p>
<p> </p>
<p> </p>
<hr />solution
<p> </p>
</div>
<div> </div>
<div>广义后缀自动机</div>
<div>其实是在trie树上建。</div>
<div>具体看</div>
<div>记录 val[i] 表示i这个状态所代表的所有串的出现次数和</div>
<div>val=(max-min)*right</div>
<div>记sum为i到根的val之和。</div>
<div>做匹配的时候，我们考虑新加入一个字符。</div>
<div>假设这个字符的匹配点是i，之前匹配长度为len。</div>
<div>那么这个字符的答案就是(len-s[fa].max)*ri[i]+s[fa].sum.</div>
<div>也就是该字符串在这个点的匹配长度，加上父亲点的sum，也就是以这个字符结尾的其他后缀的贡献。</div>
<div>
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<pre><span style="color:#008080;"> 1</span> <span style="color:#000000;">格式化代码 
</span><span style="color:#008080;"> 2</span> #include&lt;cstdio&gt;
<span style="color:#008080;"> 3</span> #include&lt;iostream&gt;
<span style="color:#008080;"> 4</span> #include&lt;cstdlib&gt;
<span style="color:#008080;"> 5</span> #include&lt;cstring&gt;
<span style="color:#008080;"> 6</span> #include&lt;algorithm&gt;
<span style="color:#008080;"> 7</span> #include&lt;cmath&gt;
<span style="color:#008080;"> 8</span> <span style="color:#0000ff;">#define</span> maxn 800005
<span style="color:#008080;"> 9</span> <span style="color:#0000ff;">#define</span> ll long long
<span style="color:#008080;">10</span> <span style="color:#0000ff;">using</span> <span style="color:#0000ff;">namespace</span><span style="color:#000000;"> std;
</span><span style="color:#008080;">11</span> <span style="color:#0000ff;">int</span> n,id[maxn],rt=<span style="color:#800080;">1</span>,cnt=<span style="color:#800080;">1</span>,la=<span style="color:#800080;">1</span><span style="color:#000000;">,a[maxn];
</span><span style="color:#008080;">12</span> <span style="color:#0000ff;">struct</span><span style="color:#000000;"> node{
</span><span style="color:#008080;">13</span>     <span style="color:#0000ff;">int</span> nex[<span style="color:#800080;">26</span><span style="color:#000000;">],par,Max,ri;
</span><span style="color:#008080;">14</span> <span style="color:#000000;">    ll val,sum;
</span><span style="color:#008080;">15</span> }s[maxn*<span style="color:#800080;">3</span><span style="color:#000000;">];
</span><span style="color:#008080;">16</span> <span style="color:#0000ff;">char</span> ch[maxn*<span style="color:#800080;">10</span><span style="color:#000000;">];
</span><span style="color:#008080;">17</span> <span style="color:#000000;">ll tax[maxn];
</span><span style="color:#008080;">18</span> <span style="color:#0000ff;">void</span> ins(<span style="color:#0000ff;">int</span> fa,<span style="color:#0000ff;">int</span> c,<span style="color:#0000ff;">int</span><span style="color:#000000;"> i){
</span><span style="color:#008080;">19</span>     
<span style="color:#008080;">20</span>     <span style="color:#0000ff;">int</span> np=++cnt,p=id[fa];s[np].ri=<span style="color:#800080;">1</span><span style="color:#000000;">;
</span><span style="color:#008080;">21</span>     <span style="color:#008000;">//</span><span style="color:#008000;">cout&lt;&lt;i&lt;&lt;' '&lt;&lt;c&lt;&lt;' '&lt;&lt;p&lt;&lt;endl;</span>
<span style="color:#008080;">22</span>     s[np].Max=s[la].Max+<span style="color:#800080;">1</span>;id[i]=la=np;<span style="color:#008000;">//</span><span style="color:#008000;">这里还不是很懂为什么是la</span>
<span style="color:#008080;">23</span>     
<span style="color:#008080;">24</span>     <span style="color:#0000ff;">for</span>(;p&amp;&amp;!s[p].nex[c];p=s[p].par)s[p].nex[c]=<span style="color:#000000;">np;
</span><span style="color:#008080;">25</span>     <span style="color:#0000ff;">if</span>(!p)s[np].par=<span style="color:#000000;">rt;
</span><span style="color:#008080;">26</span>     <span style="color:#0000ff;">else</span><span style="color:#000000;"> {
</span><span style="color:#008080;">27</span>         <span style="color:#0000ff;">int</span> q=<span style="color:#000000;">s[p].nex[c];
</span><span style="color:#008080;">28</span>         <span style="color:#0000ff;">if</span>(s[q].Max==s[p].Max+<span style="color:#800080;">1</span>)s[np].par=<span style="color:#000000;">q;
</span><span style="color:#008080;">29</span>         <span style="color:#0000ff;">else</span><span style="color:#000000;"> {
</span><span style="color:#008080;">30</span>             <span style="color:#0000ff;">int</span> nq=++<span style="color:#000000;">cnt;
</span><span style="color:#008080;">31</span>             <span style="color:#0000ff;">for</span>(<span style="color:#0000ff;">int</span> i=<span style="color:#800080;">0</span>;i&lt;<span style="color:#800080;">26</span>;i++)s[nq].nex[i]=<span style="color:#000000;">s[q].nex[i];
</span><span style="color:#008080;">32</span>             s[nq].par=s[q].par;s[nq].Max=s[p].Max+<span style="color:#800080;">1</span><span style="color:#000000;">;
</span><span style="color:#008080;">33</span>             s[q].par=s[np].par=<span style="color:#000000;">nq;
</span><span style="color:#008080;">34</span>             <span style="color:#0000ff;">for</span>(;s[p].nex[c]==q;p=s[p].par)s[p].nex[c]=<span style="color:#000000;">nq;
</span><span style="color:#008080;">35</span> <span style="color:#000000;">        }
</span><span style="color:#008080;">36</span> <span style="color:#000000;">    }
</span><span style="color:#008080;">37</span> <span style="color:#000000;">}
</span><span style="color:#008080;">38</span> <span style="color:#0000ff;">void</span><span style="color:#000000;"> Calc(){
</span><span style="color:#008080;">39</span>     <span style="color:#0000ff;">for</span>(<span style="color:#0000ff;">int</span> i=<span style="color:#800080;">1</span>;i&lt;=cnt;i++)tax[s[i].Max]++<span style="color:#000000;">;
</span><span style="color:#008080;">40</span>     <span style="color:#0000ff;">for</span>(<span style="color:#0000ff;">int</span> i=<span style="color:#800080;">1</span>;i&lt;=cnt;i++)tax[i]+=tax[i-<span style="color:#800080;">1</span><span style="color:#000000;">];
</span><span style="color:#008080;">41</span>     <span style="color:#0000ff;">for</span>(<span style="color:#0000ff;">int</span> i=<span style="color:#800080;">1</span>;i&lt;=cnt;i++)a[tax[s[i].Max]--]=<span style="color:#000000;">i;
</span><span style="color:#008080;">42</span>     <span style="color:#0000ff;">for</span>(<span style="color:#0000ff;">int</span> i=cnt;i&gt;=<span style="color:#800080;">1</span>;i--<span style="color:#000000;">){
</span><span style="color:#008080;">43</span>         <span style="color:#0000ff;">int</span> k=a[i],f=<span style="color:#000000;">s[k].par;
</span><span style="color:#008080;">44</span>         s[f].ri+=<span style="color:#000000;">s[k].ri;
</span><span style="color:#008080;">45</span>         s[k].val=s[k].ri*(s[k].Max-<span style="color:#000000;">s[f].Max); 
</span><span style="color:#008080;">46</span> <span style="color:#000000;">    }
</span><span style="color:#008080;">47</span>     <span style="color:#0000ff;">for</span>(<span style="color:#0000ff;">int</span> i=<span style="color:#800080;">1</span>;i&lt;=cnt;i++<span style="color:#000000;">){
</span><span style="color:#008080;">48</span>         <span style="color:#0000ff;">int</span> k=<span style="color:#000000;">a[i];
</span><span style="color:#008080;">49</span>         s[k].sum=s[k].val+<span style="color:#000000;">s[s[k].par].sum;
</span><span style="color:#008080;">50</span> <span style="color:#000000;">    }
</span><span style="color:#008080;">51</span> <span style="color:#000000;">}
</span><span style="color:#008080;">52</span> <span style="color:#0000ff;">int</span><span style="color:#000000;"> main(){
</span><span style="color:#008080;">53</span>     cin&gt;&gt;n;id[<span style="color:#800080;">1</span>]=<span style="color:#800080;">1</span><span style="color:#000000;">;
</span><span style="color:#008080;">54</span>     <span style="color:#0000ff;">for</span>(<span style="color:#0000ff;">int</span> i=<span style="color:#800080;">2</span>,fa;i&lt;=n;i++<span style="color:#000000;">){
</span><span style="color:#008080;">55</span>         <span style="color:#0000ff;">char</span> c;scanf(<span style="color:#800000;">"</span><span style="color:#800000;">%d %c</span><span style="color:#800000;">"</span>,&amp;fa,&amp;<span style="color:#000000;">c);
</span><span style="color:#008080;">56</span>         ins(fa,c-<span style="color:#800000;">'</span><span style="color:#800000;">a</span><span style="color:#800000;">'</span><span style="color:#000000;">,i);
</span><span style="color:#008080;">57</span> <span style="color:#000000;">    }
</span><span style="color:#008080;">58</span> <span style="color:#000000;">    Calc();
</span><span style="color:#008080;">59</span>     scanf(<span style="color:#800000;">"</span><span style="color:#800000;">%s</span><span style="color:#800000;">"</span>,ch);<span style="color:#0000ff;">int</span> l=strlen(ch),len=<span style="color:#800080;">0</span><span style="color:#000000;">;
</span><span style="color:#008080;">60</span>     <span style="color:#0000ff;">int</span> p=rt;ll ans=<span style="color:#800080;">0</span><span style="color:#000000;">;
</span><span style="color:#008080;">61</span>     <span style="color:#0000ff;">for</span>(<span style="color:#0000ff;">int</span> i=<span style="color:#800080;">0</span>;i&lt;l;i++<span style="color:#000000;">){
</span><span style="color:#008080;">62</span>         <span style="color:#0000ff;">for</span>(;!s[p].nex[ch[i]-<span style="color:#800000;">'</span><span style="color:#800000;">a</span><span style="color:#800000;">'</span>]&amp;&amp;p;p=s[p].par,len=<span style="color:#000000;">s[p].Max);
</span><span style="color:#008080;">63</span>         <span style="color:#0000ff;">if</span>(!p)p=rt,len=<span style="color:#800080;">0</span><span style="color:#000000;">;
</span><span style="color:#008080;">64</span>         <span style="color:#0000ff;">else</span><span style="color:#000000;"> {
</span><span style="color:#008080;">65</span>             p=s[p].nex[ch[i]-<span style="color:#800000;">'</span><span style="color:#800000;">a</span><span style="color:#800000;">'</span>];len++<span style="color:#000000;">;
</span><span style="color:#008080;">66</span>             <span style="color:#0000ff;">int</span> f=<span style="color:#000000;">s[p].par;
</span><span style="color:#008080;">67</span>             ans=ans+s[f].sum+(len-s[f].Max)*<span style="color:#000000;">s[p].ri;
</span><span style="color:#008080;">68</span> <span style="color:#000000;">        }
</span><span style="color:#008080;">69</span> <span style="color:#000000;">    }
</span><span style="color:#008080;">70</span>     cout&lt;&lt;ans&lt;&lt;<span style="color:#000000;">endl;
</span><span style="color:#008080;">71</span>     <span style="color:#0000ff;">return</span> <span style="color:#800080;">0</span><span style="color:#000000;">;
</span><span style="color:#008080;">72</span> }</pre>
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                    2009年12月                    <span class="count float-right">12篇</span>
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                    2009年9月                    <span class="count float-right">7篇</span>
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                    2009年8月                    <span class="count float-right">7篇</span>
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                    2009年7月                    <span class="count float-right">12篇</span>
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                    2009年5月                    <span class="count float-right">11篇</span>
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                    2009年4月                    <span class="count float-right">6篇</span>
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                    2009年2月                    <span class="count float-right">8篇</span>
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                    2009年1月                    <span class="count float-right">7篇</span>
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                    2008年12月                    <span class="count float-right">11篇</span>
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                    2008年11月                    <span class="count float-right">5篇</span>
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                    2008年10月                    <span class="count float-right">4篇</span>
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                    2008年8月                    <span class="count float-right">9篇</span>
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                    2008年7月                    <span class="count float-right">8篇</span>
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                    2008年5月                    <span class="count float-right">5篇</span>
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                    2008年4月                    <span class="count float-right">5篇</span>
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                    2008年3月                    <span class="count float-right">5篇</span>
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                    2008年2月                    <span class="count float-right">2篇</span>
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                    2008年1月                    <span class="count float-right">11篇</span>
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                    2007年12月                    <span class="count float-right">2篇</span>
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                    2007年11月                    <span class="count float-right">6篇</span>
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                    2007年10月                    <span class="count float-right">3篇</span>
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                    2007年9月                    <span class="count float-right">7篇</span>
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                    2007年8月                    <span class="count float-right">4篇</span>
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                    2007年7月                    <span class="count float-right">5篇</span>
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                    2007年6月                    <span class="count float-right">1篇</span>
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                    2007年5月                    <span class="count float-right">7篇</span>
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                    2007年4月                    <span class="count float-right">4篇</span>
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                    2007年3月                    <span class="count float-right">3篇</span>
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                    2007年2月                    <span class="count float-right">1篇</span>
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                    2007年1月                    <span class="count float-right">4篇</span>
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                    2006年12月                    <span class="count float-right">8篇</span>
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                    2006年11月                    <span class="count float-right">3篇</span>
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                    2006年10月                    <span class="count float-right">4篇</span>
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                    2006年9月                    <span class="count float-right">6篇</span>
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                    2006年8月                    <span class="count float-right">4篇</span>
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                    2006年5月                    <span class="count float-right">3篇</span>
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                    2006年4月                    <span class="count float-right">6篇</span>
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                    2006年3月                    <span class="count float-right">5篇</span>
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                    2005年9月                    <span class="count float-right">3篇</span>
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                    2005年3月                    <span class="count float-right">3篇</span>
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                    2005年2月                    <span class="count float-right">3篇</span>
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                    2004年12月                    <span class="count float-right">2篇</span>
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                    2004年11月                    <span class="count float-right">3篇</span>
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                    2004年9月                    <span class="count float-right">1篇</span>
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